A complete algorithm for counting real solutions of polynomial systems of equations and inequalities.

DOI10.1016/S0898-1221(02)00178-5zbMath1035.65054OpenAlexW1972268480MaRDI QIDQ1416272

Xiaorong Hou, Bican Xia

Publication date: 14 December 2003

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(02)00178-5

zbMATH Keywords

AlgorithminequalitiesComputer algebraResultantPolynomial systemmapleReal root-counting

Mathematics Subject Classification ID

Related Items (11)

Analyzing the dual space of the saturated ideal of a regular set and the local multiplicities of its zeros ⋮ Condition number based complexity estimate for solving polynomial systems ⋮ Solving parametric piecewise polynomial systems ⋮ Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification ⋮ Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis ⋮ Real solution isolation with multiplicity of zero-dimensional triangular systems ⋮ Properties of regular systems and algorithmic improvements for regular decomposition ⋮ Counting positive solutions for polynomial systems with real coefficients ⋮ Widely applicable periodicity results for higher order difference equations ⋮ Condition number based complexity estimate for computing local extrema ⋮ A FLAT LAGUERRE PLANE OF KLEINEWILLINGHÖFER TYPE V

Uses Software

• Maple
• DISCOVERER

Cites Work

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• Decomposing polynomial systems into simple systems
• Mechanical theorem proving in geometries. Basic principles. Transl. from the Chinese by Xiaofan Jin and Dongming Wang
• An elimination method for polynomial systems
• On the theories of triangular sets
• Recent advances on determining the number of real roots of parametric polynomials
• Which Triangles are Plane Sections of Regular Tetrahedra?

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